{
  "abstract": "Scalar travel-time relations can identify propagation geometry without velocity inputs, ray labels or equation supervision during learning. Physical interpretation is applied after learning through the high-frequency isotropic eikonal relation (Aki and Richards, 2002). Here we show that local value differences constrain derivatives through sampling geometry and smoothness. Controlled neural fields recover propagation directions with $5.34\\pm0.07^{\\circ}$ median angular error, and local P- and S-wave velocities in a prospectively locked, test-sealed realization. Classical representations also recover geometry. Scalar-matched perturbations separate value accuracy from derivative reliability; regularized inversion can recover structure when direct gradients fail. A field trained on 2.90 million Chinese arrivals retains continental crust--mantle boundary structure: correlation with a withheld reference is $ρ=0.910$ raw and 0.592 after quadratic detrending (spatial-shift $p=0.020$). Direct catalogue values yield $ρ=0.909$, and thickness contrasts are compressed. Manual-only California arrivals support broad velocity organization with limited lateral fidelity. Synthetic quantum fields containing phase information support probability-flow and trajectory readouts without supervising those quantities. These results establish conditional identification across representations and physical settings: informative scalar relations can constrain geometry, while known physical relations supply its interpretation. They do not imply that accurate scalar fitting alone guarantees reliable physical derivatives.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31238",
  "author_total": 1,
  "authors": [
    {
      "name": "Ziye Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bwd22kwwdbqyc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31238",
  "fulltext_url": null,
  "id": "bwd22kwwdbqyc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31238",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.geo-ph"
    ],
    [
      "openalex",
      "1908|Seismic Imaging and Inversion Techniques"
    ]
  ],
  "openalex": "W7214669748",
  "pdf_url": "https://arxiv.org/pdf/2609.31238",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bwd22kwwdbqyc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2609.31238",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31238"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "arxiv:physics.geo-ph",
      "subfield": "geophysics"
    }
  ],
  "title": "Wave-Propagation Geometry Emerges from Scalar Travel-Time Relations",
  "title_text": "Wave-Propagation Geometry Emerges from Scalar Travel-Time Relations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:52Z",
  "url": "https://research.draconitic.com/paper/bwd22kwwdbqyc",
  "venue": "arXiv",
  "versions": []
}